Pentagon (EntityTopic, 12)
From Hi.gher. Space
(Difference between revisions)
(polytope explorer integration) |
Username5243 (Talk | contribs) |
||
Line 3: | Line 3: | ||
| name=Pentagon | | name=Pentagon | ||
| dim=2 | | dim=2 | ||
- | | elements=5, 5 | + | | elements=5 [[digon]]s, 5 [[point]]s |
| genus=0 | | genus=0 | ||
| ssc=G5 | | ssc=G5 | ||
Line 9: | Line 9: | ||
| extra={{STS Matrix| | | extra={{STS Matrix| | ||
5 0 | 5 0 | ||
- | 1 1}}{{STS Uniform polytope | + | 1 1}}{{STS Polytope |
+ | | bowers=Peg | ||
+ | | dual=''Self-dual''}}{{STS Uniform polytope | ||
| schlaefli={5} | | schlaefli={5} | ||
- | | vfigure=[[Digon]], length | + | | dynkin=x5o |
- | + | | vfigure=[[Digon]], length (1+√5)/2 | |
}}}} | }}}} | ||
The '''pentagon''' can be seen as the two-dimensional analog to the [[dodecahedron]] in 3D and the [[cosmochoron]] in 4D. It is also the lowest-dimensional member of the [[ursatope]]s, with a (trivial) [[digon]]al base. | The '''pentagon''' can be seen as the two-dimensional analog to the [[dodecahedron]] in 3D and the [[cosmochoron]] in 4D. It is also the lowest-dimensional member of the [[ursatope]]s, with a (trivial) [[digon]]al base. |
Revision as of 01:42, 26 March 2017
The pentagon can be seen as the two-dimensional analog to the dodecahedron in 3D and the cosmochoron in 4D. It is also the lowest-dimensional member of the ursatopes, with a (trivial) digonal base.
Equations
- The hypervolumes of a pentagon with side length l are given by:
total edge length = 5l
area = 1∕4 · √(25+10√5) · l2
Incidence matrix
Usage as facets
- 12× 1-facets of a dodecahedron
- 12× 1-facets of a rhodomesohedron
- prism: 2× 1-facets of a pentagonal prism
- 12× 1-facets of a truncated icosahedron
- pyramid: 1× 1-facets of a pentagonal pyramid
- 12× 1-facets of a rhodoperihedron
- 60× 1-facets of a pentagonal hexecontahedron
- 24× 1-facets of a pentagonal icositetrahedron
- 12× 1-facets of a snub dodecahedron
- 6× 1-facets of a associahedron
- 4× 1-facets of a digon-unpinched pentagonal prism
- 1× 1-facets of a pentagonal cupola
- 3× 1-facets of a tridiminished icosahedron (named pen)
- 4× 1-facets of a bilunabirotunda
- 2× 1-facets of a hexagonal pyrawedge
- 2× 1-facets of a (dual of metabidiminished icosahedron)
- 1× 1-facets of a digon-unpinched square pyramid
- 2× 1-facets of a metabidiminished icosahedron (named rroob)
- 3× 1-facets of a triangular hebesphenorotunda (named pen)
- 1× 1-facets of a parabiorthotriangulated orthopinched triangular cupola
- 1× 1-facets of a pentagonal cupolawedge
- 1× 1-facets of a pentagonal transcupolawedge
- 2× 1-facets of a square transcupolawedge (named ryopc)
- 1× 1-facets of a triangulated pinched triangular cupola (named white)
- 720× 2-facets of a cosmochoron
- 72× 2-facets of a bixylodiminished hydrochoron (named pentagons)
- 288× 2-facets of a rectified snub demitesseract
- 24× 2-facets of a castellated rhodoperihedral prism
- 60× 2-facets of a castellated rhodoperihedral prism
- 12× 2-facets of a D4.3.1 dual
- 288× 2-facets of a truncated snub demitesseract
- 96× 2-facets of a D4.11
- 4× 2-facets of a bilunabirotunda pseudopyramid
- 24× 2-facets of a castellated rhodopantohedral prism (named 5 horz)
- 120× 2-facets of a castellated rhodopantohedral prism (named 2-2 vert)
- 3× 2-facets of a D4.16
- 3× 2-facets of a triangular hebesphenorotunda pseudopyramid (named pen)
- 12× 2-facets of a (dual of triangular hebesphenorotundaeic rhombochoron)
- 12× 2-facets of a triangular hebesphenorotundaeic rhombochoron (named ggbbp)
- 12× 2-facets of a triangular hebesphenorotundaeic rhombochoron (named rroob)
- 12× 2-facets of a (dual of tetraaugmented triangular hebesphenorotundaeic rhombochoron)
- 24× 2-facets of a (dual of tetraaugmented triangular hebesphenorotundaeic rhombochoron)
- 12× 2-facets of a tetraaugmented triangular hebesphenorotundaeic rhombochoron (named ggbbp)
- 24× 2-facets of a D4.7 (named rcbpp)
- 12× 2-facets of a D4.7 (named ooyyg)
- 12× 2-facets of a D4.7 (named pppps)
Notable Dishapes | |
Flat: | triangle • square • pentagon • hexagon • octagon • decagon |
Curved: | circle |